location fingerprinting for uwband systems

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Diss. ETH No. 19147

Location Fingerprinting for

Ultra-Wideband Systems

The Key to Efficient and Robust Localization

A dissertation submitted to the

ETH Zurich

for the degree of

Doctor of Sciences (Dr. sc. ETH Zurich)

presented by

CHRISTOPH STEINER

Dipl.-Ing., Graz University of Technology

born March 11, 1980

citizen of Austria

accepted on the recommendation of

Prof. Dr. Armin Wittneben, examiner

Prof. Dr. Moe Z. Win, co-examiner

2010


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Danke

An dieser Stelle mchte ich mich bei all denen bedanken, die zum Gelingen dieser Arbeit

beigetragen haben.

Lieber Armin, ich mchte mich ganz besonders bei dir bedanken. Ich erinnere mich an

viele interessante Gesprche mit dir und - was mich nach wie vor fasziniert - nach jedem

Gesprch habe ich die Dinge strukturierter gesehen und darber hinaus eine Handvoll neuer

Ideen mitbekommen. Ich bewundere deine freundschaftliche und frhliche Art, deine Moti-

vationsknste und deine Energie. Vielen Dank fr deine ausgezeichnete Betreuung!

Dear Professor Moe Z. Win, I would like to thank you for being my co-examiner and

reviewing my PhD thesis. I am honored.

Dear Georgios and dear Celal, I am very happy that we three shared an office for almost

five years. I will remember our numerous interesting discussions on the white board, our

activities outside the office, and - of course - seemingly endless phone conversations in Greek

and Turkish.

Lieber Oliver, es hat mich auch sehr gefreut, mit dir das Bro fr fast zwei Jahre zu teilen.

Schade, dass wir nicht mehr regelmig Klettern gehen knnen.

Lieber Heinrich, lieber Florian, lieber Thomas und lieber Frank, ich bin sehr froh mit euch

in der UWB Gruppe zusammengearbeitet zu haben. Gemeinsam haben wir viel erreicht und

dabei jede Menge Spa gehabt.

Special thanks go to Claudia, Barbara, Azadeh, Marc, Jrg, Gabriel, Ingmar, Boris, Eti-enne, Stefan, Jian, Raphael, Zemene, Eric, Carlo and Christoph. You have been and are great

colleagues!

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Abstract

In this thesis, a novel position location concept is proposed and studied, which provides

accurate position estimates in dense multipath and non-line-of-sight propagation environ-

ments. The main idea is to apply the location fingerprinting paradigm of position location

to channel impulse responses with ultra-wide bandwidth. The large bandwidth enables afine temporal resolution of the multipath propagation channel, which in turn acts as a unique

location fingerprint of the positions of transmitter and receiver.

In the first part of this thesis, a location fingerprinting framework is developed from a com-

munication theoretic perspective. The position location problem is formulated as hypothesis

testing problem, such that fundamental methods from statistical detection theory can be ap-

plied. Location fingerprints are modeled by parameterized probability density functions.

Different hypotheses are distinguished by these parameters, which have to be estimated dur-

ing a training phase. This framework generalizes a wide class of location fingerprinting ap-

proaches and enables the systematic derivation of optimal classification rules and theoretical

performance analysis.

In the second part, location fingerprinting with two specific ultra-wideband receiver struc-

tures is studied in detail. The first receiver is able to perform channel estimation. The

corresponding location fingerprints are chosen as Nyquist sampled versions of the estimated

channel impulse responses. The second receiver is a low complexity generalized energy

detection receiver, where the energy samples at the output of the analog front-end serve as

location fingerprints. In order to derive optimal classification rules, it is necessary to establish

a stochastic description of the location fingerprints. This stochastic modeling is performed

on the basis of measured data and a model selection criterion. The position location perfor-

mance of both receiver structures is analyzed theoretically and experimentally with measured

data. It is shown that decimeter accuracy is achievable with both receiver structures in dense

multipath and non-line-of-sight propagation environments.

However, the performance analysis reveals also a major shortcoming of the proposed

method: In order to achieve high position location accuracy, a large amount of training

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Abstract

data is required. This issue is addressed in the third part of this thesis, where two promis-

ing techniques are proposed, which increase the efficiency of the training phase. At first,

the position location problem is reformulated, such that the training phase can be combined

with the localization phase in an iterative manner. Results from the localization phase are

used as additional training data. Based on experimental performance results it is shown that

the required amount of training data can be significantly reduced. The second technique is

even more promising. Only very few measured channel impulse responses - theoretically

only three per hypothesis for two-dimensional localization - are required during the train-

ing phase for parameter estimation. This efficient training phase is based on a geometrical

channel model and exploits a priori knowledge about the geometry of the propagation envi-

ronment. An experimental performance evaluation shows the high potential of this approach

to achieve minimal training phase complexity.

The thesis concludes with a summary of the major findings and with a list of interesting

future research topics in the field of location fingerprinting for ultra-wideband systems.

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Kurzfassung

In dieser Arbeit wird eine neuartige Methode zur Ortung von drahtlosen Kommunikationsge-

rten prsentiert und analysiert. Das Verfahren verspricht eine genaue und zuverlssige Posi-

tionsbestimmung, insbesondere fr einen bertragungskanal mit dichter Mehrwegeausbrei-

tung und fr den Fall, dass keine direkte Sichtverbindung zwischen Sender und Empfnger

besteht. Die grundstzliche Idee besteht darin, die Impulsantwort des bertragungskanals

alsFingerabdruckfr die Positionen von Sender und Empfnger zu verwenden. Eine feine

zeitliche Auflsung des bertragungskanals ist dabei ausschlaggebend. Dies kann durch eine

hinreichend grosse Signalbandbreite erreicht werden. Dieser rtliche Fingerabdruck wird im

Folgenden alsLocation Fingerprintbezeichnet. Lokalisierung mittels Location Fingerprints

wirdLocation Fingerprintinggenannt.

Diese Dissertation beginnt mit der Entwicklung eines theoretischen Grundgerstes zur

systematischen Beschreibung und Analyse von Location Fingerprinting. Das Ortungspro-

blem wird als Hypothesentest formuliert, wodurch die Anwendung von Methoden aus der

statistischen Entscheidungstheorie ermglicht wird. Die stochastische Modellierung der Lo-

cation Fingerprints erfolgt ber eine parametrisierte Wahrscheinlichkeitsdichtefunktion, wo-

bei die Parameter einzelne Hypothesen voneinander unterscheiden und whrend einer Trai-

ningsphase empirisch geschtzt werden mssen. Mit diesem theoretischen Grundgerst kn-

nen viele andere, in der Literatur vorgeschlagene, Location Fingerprinting Anstze beschrie-

ben und analysiert werden. Ausserdem ermglicht dieses Grundgerst die systematische

Herleitung von optimalen Entscheidungsregeln und die theoretische Analyse von Fehler-

wahrscheinlichkeiten.

Im zweiten Teil wird die Lokalisierung mit zwei unterschiedlichen Empfngerstrukturen

behandelt. Zunchst wird ein kohrenter Empfnger betrachtet, der Kanalimpulsantworten

mit grosser Bandbreite schtzen kann. Die zeitlich gefensterte Kanalimpulsantwort wird mit

Nyquist-Rate abgetastet, um den entsprechenden Location Fingerprint zu erhalten. Als zwei-

ter Empfnger wird ein verallgemeinerter Energiedetektor untersucht. Die Abtastwerte am

Ausgang des analogen Frontends bilden den entsprechenden Location Fingerprint. Damit

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Kurzfassung

statistische Methoden angewendet und optimale Entscheidungsregeln abgeleitet werden kn-

nen, wird eine genaue stochastische Beschreibung der Location Fingerprints bentigt. Die

Auswahl des stochastischen Modells basiert auf der statistischen Analyse von gemessenen

Daten.

Die Genauigkeit und Zuverlssigkeit der Positionsbestimmung wird theoretisch und ex-

perimentell untersucht. Mit beiden Empfngerstrukturen kann in sehr vielen Fllen eine Ge-

nauigkeit im Bereich von wenigen Dezimetern erreicht werden, obwohl alle gemessenen

bertragungskanle eine dichte Mehrwegeausbreitung und einige bertragungskanle keine

direkte Sichtverbindung zwischen Sender und Empfnger aufweisen. Diese experimentelle

Analyse offenbart aber auch eine grosse Schwche: Es werden sehr viele Trainingsdaten zur

empirischen Parameterschtzung bentigt, um eine hohe Genauigkeit zu erreichen.

Der dritte Teil dieser Arbeit widmet sich dieser Schwche. Zwei vielversprechende Me-

thoden zur Verbesserung der Effizienz der Trainingsphase werden vorgestellt und analysiert.

Zunchst wird das Ortungsproblem so umformuliert, dass die Trainingsphase mit der Loka-

lisierungsphase kombiniert werden kann. Iterativ werden Resultate der Lokalisierungspha-

se dazu verwendet, um die Trainingsergebnisse zu verbessern. Bessere Trainingsergebnisse

bedeuten wiederum genauere Ortungsresultate. Die experimentelle Analyse zeigt, dass die

bentigte Anzahl an Trainingsdaten dadurch erheblich reduziert werden kann. Die zweite

Methode ist noch vielversprechender. Theoretisch werden fr eine zweidimensionale Loka-

lisierung nur drei gemessene Kanalimpulsantworten pro Hypothese zur Parameterschtzung

whrend der Trainingsphase bentigt. Diese effiziente Trainingsphase basiert auf einem geo-

metrischen Kanalmodell und nutzt a priori Wissen ber die Geometrie des Raumes. Eine

experimentelle Analyse dieser Parameterschtzmethode zeigt deren grosses Potential, um

die Komplexitt der Trainingsphase auf ein Minimum zu reduzieren.

Als Abschluss dieser Abhandlung werden alle Ergebnisse resmiert, Schlussfolgerungen

gezogen, und interessante weiterfhrende Forschungsfragen diskutiert.

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Contents

Danke i

Abstract iii

Kurzfassung v

1 Introduction 1

1.1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Ultra-Wideband Wireless Communication . . . . . . . . . . . . . . . . . . 2

1.3 Ultra-Wideband Positioning Systems. . . . . . . . . . . . . . . . . . . . . 2

1.3.1 Geometric Position Location . . . . . . . . . . . . . . . . . . . . . 3

1.3.2 Location Fingerprinting . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Location Fingerprinting: A Communication Theoretic Perspective 9

2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Deterministic Location Fingerprints . . . . . . . . . . . . . . . . . . . . . 11

2.3 Novel Position Location Concept - "Geo-Regioning" . . . . . . . . . . . . 12

2.4 Location Fingerprinting as Hypothesis Testing Problem . . . . . . . . . . 14

2.4.1 Average Positioning Error . . . . . . . . . . . . . . . . . . . . . . 15

2.4.2 Total Probability of Error. . . . . . . . . . . . . . . . . . . . . . . 152.4.3 Location Fingerprinting with Multiple Observations per Agent . . . 17

2.4.4 Pairwise Error Probabilities . . . . . . . . . . . . . . . . . . . . . 17

3 Channel Measurement Campaign 19

3.1 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Measurement Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 Impact of Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Measurement Signal-to-Noise Ratio . . . . . . . . . . . . . . . . . . . . . 22

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3.5 Energy Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.6 Temporal Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.6.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 233.6.2 Maximum Absolute Value Alignment . . . . . . . . . . . . . . . . 24

4 Location Fingerprinting with a Coherent Receiver 25

4.1 Choice of the Location Fingerprints . . . . . . . . . . . . . . . . . . . . . 26

4.2 Regional Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2.1 Marginal Distribution of Channel Taps . . . . . . . . . . . . . . . 28

4.2.2 Second Order Statistics . . . . . . . . . . . . . . . . . . . . . . . 35

4.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Distortions of the Location Fingerprints . . . . . . . . . . . . . . . . . . . 39

4.3.1 Antenna Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3.2 Thermal Noise and Time Variations . . . . . . . . . . . . . . . . . 40

4.4 Position Location and Clustering Systems . . . . . . . . . . . . . . . . . . 41

4.4.1 Training Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.4.2 Localization Phase . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5 Analytical Pairwise Error Probabilities . . . . . . . . . . . . . . . . . . . 43

4.6 Theoretical and Experimental Performance Analysis . . . . . . . . . . . . 47

4.6.1 Randomized Cross-Validation Method . . . . . . . . . . . . . . . 48

4.6.2 Default System Parameters . . . . . . . . . . . . . . . . . . . . . 48

4.6.3 Number of Training Signals . . . . . . . . . . . . . . . . . . . . . 49

4.6.3.1 Analytical Results . . . . . . . . . . . . . . . . . . . . . 49

4.6.3.2 Experimental Results . . . . . . . . . . . . . . . . . . . 52

4.6.4 Conditional and Pairwise Error Probabilities . . . . . . . . . . . . 53

4.6.5 Distortion Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.6.6 Signal Bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.6.7 Observation Window Size . . . . . . . . . . . . . . . . . . . . . . 57

4.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5 Location Fingerprinting with a Generalized Energy Detection Receiver 59

5.1 Generalized Energy Detection Receiver . . . . . . . . . . . . . . . . . . . 60

5.1.1 Choice of the Location Fingerprints . . . . . . . . . . . . . . . . . 61

5.1.2 System Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Exact Distribution of Energy Samples for a Gaussian Channel Model. . . . 62

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5.3 Stochastic Modeling of Energy Samples . . . . . . . . . . . . . . . . . . . 65

5.3.1 Gaussian Channel Model . . . . . . . . . . . . . . . . . . . . . . . 66

5.3.2 Measured Channel Impulse Responses. . . . . . . . . . . . . . . . 69

5.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.4 Correlation among Energy Samples . . . . . . . . . . . . . . . . . . . . . 72

5.4.1 Empirical Correlation Matrices. . . . . . . . . . . . . . . . . . . . 73

5.4.2 Analytical Expression for Correlation Coefficients . . . . . . . . . 73


5.5.1 Training Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75


5.6 Accuracy of Closed Form Approximations . . . . . . . . . . . . . . . . . 77

5.7 Experimental Performance Analysis . . . . . . . . . . . . . . . . . . . . . 79

5.7.1 Default System Parameters . . . . . . . . . . . . . . . . . . . . . . 79

5.7.2 Number of Training Vectors . . . . . . . . . . . . . . . . . . . . . 80

5.7.3 Distortion Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.7.4 Sampling Frequency of Energy Detector. . . . . . . . . . . . . . . 81

5.7.5 Number of Regions . . . . . . . . . . . . . . . . . . . . . . . . . 82


6 Combination of Training Phase and Localization Phase 85

6.1 Location Fingerprinting via Parameter Estimation of Mixture Densities . . 86

6.2 Expectation Maximization Algorithm . . . . . . . . . . . . . . . . . . . . 87

6.2.1 Maximum Likelihood Parameter Estimation for Mixture Densities . 87

6.2.2 Gaussian Mixture Densities . . . . . . . . . . . . . . . . . . . . . 89


6.3.1 Training Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90


6.4 Experimental Performance Analysis . . . . . . . . . . . . . . . . . . . . . 936.4.1 Singular Initial Covariance Matrices . . . . . . . . . . . . . . . . . 94

6.4.2 Number of Training SignalsLand ObservationsLb . . . . . . . . . 96

6.4.3 Multiple Observations per Agent. . . . . . . . . . . . . . . . . . . 97


7 Efficient Training Phase 101

7.1 Electromagnetic Wave Propagation . . . . . . . . . . . . . . . . . . . . . 101

7.2 Input Output Relations in Passband and Equivalent Baseband . . . . . . . . 104

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7.3 Analysis of Path Delays. . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.3.1 Geometrical Description of Interacting Objects . . . . . . . . . . . 105

7.3.2 Nonlinear Mapping of Transmitter Position on Path Delays. . . . . 105

7.3.3 Upper Bound on Path Delay Variation . . . . . . . . . . . . . . . . 108

7.3.4 Linearization of Path Delays . . . . . . . . . . . . . . . . . . . . . 108

7.3.5 Temporal Alignment . . . . . . . . . . . . . . . . . . . . . . . . . 113

7.4 Linearization of Path Gains . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.5 Simplified Input Output Relation . . . . . . . . . . . . . . . . . . . . . . . 115

7.6 Estimation of Linear Model Parameters . . . . . . . . . . . . . . . . . . . 116

7.6.1 Joint Estimation of Path Gains and Path Delays . . . . . . . . . . . 116

7.6.2 Least Squares Estimation ofLM . . . . . . . . . . . . . . . . . . 118

7.6.3 The Path Pairing Problem . . . . . . . . . . . . . . . . . . . . . . 120

7.7 Experimental Analysis of Prediction Accuracy . . . . . . . . . . . . . . . 122

7.7.1 Measurement Campaign in Anechoic Chamber . . . . . . . . . . . 122

7.7.2 Figures of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.7.3 Performance Results . . . . . . . . . . . . . . . . . . . . . . . . . 126

7.8 Parameter Estimation based on Predicted Channel Responses . . . . . . . . 131


8 Conclusions and Outlook 1358.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

8.2 Outlook on Future Research . . . . . . . . . . . . . . . . . . . . . . . . . 137

A Distance Matrix for UWB Channel Measurement Campaign 139

B Akaikes Information Criterion 141

C Derivation of Approximation (5.5) 145

D Wishart Distribution 149

E Expectation of the Product of Four Gaussian Random Variables 151

Acronyms 153

Notation 155

Bibliography 157

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Chapter 1

Introduction

1.1 Motivation

Position location information is essential for the emergence of applications that will revo-

lutionize the daily life of many people: Starting from monitoring of fire fighters and police

men, over precise and ubiquitous equipment tracking, up to the surveillance of swarm be-

havior [14]. It is of particular interest for communication engineers that position location

information opens a new dimension - or rather three new dimensions - which can be exploited

for optimization of various figures of merit such as bit error probability of a communicationlink [5], interference mitigation in wireless networks, or delay and throughput of routing

algorithms.

Nowadays, high localization accuracy is still an ambitious goal in dense multipath and

non-line-of-sight (LoS)propagation environments for state-of-the-art position location ap-

proaches [3, 6]. However, exactly such environments will prevail in most of the aforemen-

tioned application scenarios, which makes it essential to invent and explore novel position

location methods featuring good performance in such harsh propagation environments.

Furthermore, low complexity is a key requirement for a ubiquitous implementation of po-

sition location systems. In the context of localization the term complexity subsumes the

required position location infrastructure, necessary a priori knowledge, additional hardware

requirements forreceivers (RXs)andtransmitters (TXs),and processing power of localiza-

tion algorithms.

The unreliability of state-of-the-art localization methods in dense multipath and non-LoS

propagation environments and the need for low complexity position location systems mo-

tivate the research presented in this thesis. The ultimate goal is a robust localization or

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Chapter 1 Introduction

clustering1 method, which provides accurate position location information or cluster infor-

mation with affordable complexity merely as a side product of data transmission between

wireless nodes.

1.2 Ultra-Wideband Wireless Communication

Ultra-wideband (UWB)communication systems are thoroughly discussed in [79]. We re-

call important advantages over conventional narrowband communication systems, which

motivate the consideration ofUWBsignals for position location.UWBsystems are allowed

to transmit license-freein the spectrum from 3.1GHz to10.6GHz with regulated transmit

power [10]. Since the spectrum can be used for free, a lot of new applications requiringcheap wireless communication are supported. It is expected that most of these applications

benefit additionally from position location information. Furthermore, the large bandwidth of

several GHz enables very high data rates and, with that, the possibility to design ultra low

power transceivers by exploiting low duty-cycle communication [11]. Ultra low power con-

sumption supports the emergence of applications requiring mobile, battery powered wireless

devices. Altogether it is envisioned that a lot of cheapUWBtransceivers will coexist and

form an ad-hoc wireless network. It is of essential importance, from the application perspec-

tive and from the network management perspective, that the positions of these transceivers

can be estimated accurately and with low complexity.

1.3 Ultra-Wideband Positioning Systems

The research presented in this thesis focuses on indoor position location and clustering for

short range wireless communication systems usingradio frequency (RF)signals with ultra-

wide bandwidths. However, many theoretical concepts are introduced in a generic way,

which makes them immediately applicable to other research areas such as ultrasound signalsor underwater communication. The objective of position location systems is the estimation of

the unknown positions of wireless nodes denoted asagentsbased on a set of observations at

or from reference nodes with known positions denoted asanchors2. In general, the following

two position location scenarios can be distinguished [12]:

1Clustering of a wireless network is defined as the process of grouping nodes into clusters based on a certaindistance measure between the nodes. In this thesis, we consider Euclidian distance as distance measure,such that physically close nodes are grouped into the same cluster.

2Throughout this thesis, we refer to the agents as TXsand to the anchors asRXswithout loss of generality,because their roles are interchangeable due to channel reciprocity.

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1. Self-positioning: An agent estimates its own position based on observed RFsignals,

which have been transmitted by the anchors.

2. Remote positioning: The position of an agent is estimated by a central unit (CU),which uses the observations of the transmittedRFsignal of the agent at the anchors.

In the following two sections, two conceptually different position location techniques are

discussed. The main purpose is to review state-of-the-art position location techniques with

emphasis on their shortcomings in harsh propagation environments and on their complexity.

The interested reader is referred to the book entitled "Ultra-wideband Positioning Systems"

by Sahinoglu et al. [13], which provides a comprehensive introduction toUWBpositioning

systems in Chapter1and toUWBsignals in Chapter2.

1.3.1 Geometric Position Location

Geometric position location techniques consist of two steps. First, signal metrics3 depend-

ing on the relative positions of agent and anchor are estimated from the observed RFsig-

nals at each anchor. In the second step these metrics are used for multi-lateration or multi-

angulation, respectively [2, 14]. There exists a lower bound on the required number of an-

chors such that an unambiguous position location estimate is obtained. This lower bound is

based on geometrical considerations. For example, at least three anchors are required for un-ambiguous two-dimensional position location estimation, iftime of arrival (ToA)estimates

are used.

The algorithmic complexity of multi-lateration or multi-angulation algorithms (e.g. non-

linear least squares optimization [1517]) is well understood and for current computers

not obstructive, since the processing can be performed at a CU which is connected to

a power supply. However, the estimation of signal metrics from RFsignals at the an-

chors is performed by a wireless node, which might be just battery powered. Therefore,

there exists a large amount of research concerned with low complexity estimation ofToA,time difference of arrival (TDoA),received signal strength (RSS)orangle of arrival (AoA).

For example, low complexityToAestimation rules are proposed in [1823].

The accuracy of geometric position location techniques is determined by the

signal-to-noise ratio (SNR)of theRFsignals, the hardware abilities and processing power

of the anchors, the propagation environment, and the number of anchors. Fundamental per-

formance limits based on the Cramr-Rao lower bound and the Ziv-Zakai lower bound for3Examples for signal metrics are time of arrival, time difference of arrival, received signal strength, and angle

of arrival.

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variousRXarchitectures andRFsignals are derived in [6]. If the propagation channel has a

strongLoScomponent, then geometric position location techniques show a remarkable good

performance. The experimental demonstration of position location and tracking described

in [24] is just one example for the potential of position location based on ranging4 withUWB

signals. However, a rich multipath propagation environment and especially non-LoSchan-

nel conditions degrade the quality ofToA,TDoA,RSSandAoAmeasurements drastically.

Increasing theRFsignal bandwidth increases the robustness against multipath errors, which

implies thatUWBsignals are preferable in indoor environments [14, 25]. Despite the large

bandwidth, non-LoSsituations cause positively biasedToAandTDoAestimates [26] and

inaccurateRSSandAoAestimates. Therefore, it is essential to deploy the anchors carefully

to ensureLoSconditions for all possible agent positions. If this is not feasible, the number

of anchors must be increased at the expense of hardware and infrastructure complexity.

Recently, cooperative localization has gained a lot of attention [27, 28]. The idea is to

allow for cooperation among agents to improve the overall localization performance and

the coverage area. Signal metrics between adjacent agents are used additionally by the po-

sition location algorithms, which implies that the lower bound on the required number of

anchors does not exist anymore. Furthermore, the robustness against non-LoSsituations can

be increased, since the number ofLoScommunication links is increased with high probabil-

ity. The cooperative paradigm requires additional data transfer among agents and anchors,

which might limit the applicability of this approach.

1.3.2 Location Fingerprinting

Location fingerprinting [3,29,30] is a conceptually different position location technique,

which also consists of two phases. In phase one (training phase), the position location sys-

tem gathers coordinates of training points and related signal metrics (location fingerprints)

extracted fromRFsignals at a number of anchors and stores them into a central database.

In phase two (localization phase), the anchors observe location fingerprints of agents and

find the best matching entries in the database. There exists a large number of algorithms for

this pattern matching such as support vector machines, neural networks, weighted k near-

est neighbors, or Bayesian approaches [31, 32]. Note that in contrast to geometric position

location techniques, there does not exist a lower bound on the required number of anchors.

Thus, theoretically it is possible to locate agents unambiguously based on the observedRF

4The range information is obtained fromToA,TDoA,orRSSmeasurements.

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signal at a single anchor. Further note that location fingerprinting is a classification problem,

whereas geometric position location is a regression problem [32].

The complexity of these pattern matching (classification) algorithms is of minor impor-tance, since the processing can be done at aCUwhich is connected to a power supply. The

major part of the complexity is caused by the training phase, since location fingerprints from

the whole surveillance area5 must be gathered. An important parameter is the grid spac-

ing, which determines the total number of training points and the resolution of the spatial

quantization. The complexity of the training phase is further discussed in Chapter 2.

The performance of location fingerprinting algorithms is commonly measured with accu-

racyandprecision[30]. Accuracy measures the distance error between the estimated and the

true location and precision states the percentage of position location estimates with a certainaccuracy. The performance of location fingerprinting algorithms is mainly determined by

the grid spacing, the choice and modeling of the location fingerprints, the pattern match-

ing algorithm, the SNR of theRFsignals, the variability of the propagation environment,

and the number of anchors. Assume that the training points lie on a two-dimensional grid

with a spacing of0.2m in each dimension and that the surveillance area is an office room

with an area of5m times 5 m. In this example the total number of training points would

be(5/0.2)2 = 625. The true position of an agent is assumed to be uniformly distributed in

the uncertainty area of0.2m times 0.2m around a grid point. The figure of merit for theaccuracy is theroot mean square (RMS)error. Therefore, the lower bound on the achievable

localization accuracy would be0.2

1/6 8.2cm.The choice and modeling of location fingerprints is a very important step, which impacts

performance, complexity, and robustness of the system. ForUWBsystems there exists very

few research on this topic, which motivates the thorough treatment of this modeling problem

in this thesis. Nowadays, the most common choice for location fingerprints is RSSof Wi-Fi

signals [30, 33]. The corresponding localization systems are implemented as software add-

on to existing Wi-Fi infrastructure. There exist virtually no additional costs except for thetraining phase, since every Wi-Fi card is able to measure theRSSand the coordinates of the

Wi-Fi access points acting as anchors are known a priori. Each access point provides only

one degree of freedom (oneRSSvalue), which implies that many access points are required,

in order to achieve a satisfactorily performance. However, in contrast to geometric position

location techniques, a strongLoScomponent is not required. Experimental performance

analyses of recent location fingerprinting systems based on RSScan be found in [33, 34],

5The surveillance area subsumes all possible agent positions. Note that the surveillance area does not have tobe a connected set. Depending on the application isolated regions might be sufficient.

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where accuracies from2m to 3m for roughly two-third of all test positions are reported.

In [35], it is proposed to use seven parameters (mean excess delay,RMSdelay spread,

maximum excess delay, total received power, number of multipath components, powerof the first path, and the arrival time of the first path), which are estimated from

channel impulse responses (CIRs)with 200 MHz bandwidth, as location fingerprint. The

pattern matching algorithm is implemented with an artificial neural network using367train-

ing signals to train the neural network. The authors report an accuracy of2m for80percent

of the test cases using a single anchor. The grid spacing of the training points is 0.5m in

one direction and1m in the other direction. In [36], the authors propose to apply a wavelet

compression to extract features ofCIRswith200 MHz bandwidth and use them as location

fingerprints. Pattern matching is done again with an artificial neural network and similar

accuracy as in [35] with a precision of67percent is achieved. Note that both approaches

in [35, 36] require time synchronization betweenTXandRX.

The application of UWB signals to location fingerprinting has been first proposed in

[37, 38], where sampledCIRsare used as location fingerprints. A Bayesian approach6 is

pursued to derive amaximum likelhood (ML)pattern matching algorithm. In these works,

it is shown based on measuredCIRswith3 GHz bandwidth that excellent accuracy at high

precision can be achieved with a single anchor. These promising results have initiated the

research presented in this thesis. The authors of [39] applyUWBCIRsfor location finger-

printing in underground mines in the same way as proposed in [37,38] and report similar per-

formance results. In [40], the authors propose to useUWBCIRsin the frequency band from

3.1GHz to10.6GHz as location fingerprints. Their database consists of a high-resolution

map ofCIRs,which requires a time consuming measurement process and a large storage

capacity. A very accurate positioning device is used to measureCIRsat a grid spacing of

0.01m in each dimension. The surveillance area is 1 m times 1 m resulting in10000grid

points. The position of an agent is found by the maximization of theCIRcross-correlation

coefficient. The performance results forLoSand non-LoSsituations show a remarkable high

accuracy of around2 cm. Note that time synchronization betweenTXandRXis assumed

for the approach proposed in [40].

In general, location fingerprinting is a promising alternative to geometric position location

techniques especially in harsh indoor environments, where the propagation channel does

not have a strongLoScomponent. Provided theRFsignal bandwidth is large enough, the

multipath propagation structure, which is related to the positions of the agent and anchor,

can be exploited for position location. In case ofUWBsignals, theRFsignals at each

6Further details can be found in Chapter2.

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1.4 Contributions

anchor have already a large number of degrees of freedom, which implies that good perfor-

mance with a single anchor is achievable. This is essential for applications, which require

an operation without pre-installed infrastructure in an ad-hoc manner. An example would be

self-localization of nodes in a wireless network [41].

1.4 Contributions

In this thesis, a novel position location concept based onUWBRFsignals is proposed and

studied. The distinct advantage of this method over state-of-the-art position location solu-

tions is that accurate position estimates can be obtained in dense multipath and non-LoSpropagation environments. The main idea is to apply the location fingerprinting approach to

CIRswith an ultra-wide bandwidth, which provides an accurate temporal resolution of the

multipath propagation channel. This multipath structure is a unique fingerprint of the relative

positions ofTXandRX, i.e. agent and anchor. In a constant propagation environment, the

CIRdepends only on the positions of agent and anchor. In contrast to geometric position

location techniques, the proposed location fingerprinting system benefits from dense multi-

path propagation, because the location fingerprints at different agent positions become more

distinct. Since signal metrics related to the direct path are not required for localization, the

performance of the proposed location fingerprinting scheme is robust to non-LoSconditions.

Accurate time synchronization between anchors and agents is not required, since only the

shape of theCIRis chosen as signal metric and the absolute timing information is neglected.

First investigations of the proposed location fingerprinting approach, originally calledUWB

geo-regioning, are published in [37, 38]. The work presented in this thesis continues this

research and provides the following contributions:

In Chapter2, a location fingerprinting framework is developed from a communication

theoretic perspective. The position location problem is formulated as hypothesis testingproblem, such that methods from statistical detection theory can be applied. It is proposed to

relax the requirement of estimating the exact location of an agent to rather deciding, whether

this agent is located in a region of a certain size. Stochastic location fingerprints are assumed

and parameterizedprobability density functions (PDFs) are used to model their behavior.

An immediate consequence of this stochastic modeling approach is that the training phase

reduces to a statistical parameter estimation problem. The theoretical framework generalizes

a wide class of location fingerprinting approaches and enables the systematic derivation of

optimal classification rules and a theoretical performance analysis.

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In the second part, location fingerprinting with two specificUWB RXstructures is studied

in detail. The firstRX(cf. Chapter4) is able to perform channel estimation. The correspond-

ing location fingerprints are chosen as Nyquist sampled versions of the estimated CIRs. The

secondRXis a low complexity generalizedenergy detection (ED)RX(cf. Chapter5) and

the energy samples at the output of the analog front-end serve as location fingerprints. In

order to derive optimal classification rules it is necessary to establish a stochastic description

of the location fingerprints. This stochastic modeling is performed on the basis of measured

CIRsand a model selection criterion. These modeling results are also important for other

fields in wireless communications, such as channel modeling or RXdesign (e.g. [42]). Es-

pecially the stochastic modeling of energy samples based on measured CIRshas not been

treated so far.

The performance of both RXs is analyzed theoretically and experimentally using measured

CIRs.The corresponding channel measurement campaign is outlined in Chapter3. The im-

pact of important system parameters such asRFsignal bandwidth on the performance is

investigated. It is shown that decimeter position location accuracy is achievable for bothRX

structures in a dense multipath and non-LoSpropagation environment. However, these per-

formance investigations reveal also a major shortcoming of the proposed method: A large

amount of training data is required, in order to achieve high position location accuracy and

precision. This issue is addressed in the third part of this thesis, where two promising tech-

niques are developed, in order to increase the efficiency of the training phase. In Chapter 6,

it is proposed to combine the parameter estimation step during the training phase with the

localization phase, in order to iteratively improve the quality of the parameter estimates and

the position location accuracy. It is shown with experimental performance results that the

required amount of training data can be significantly reduced.

The second technique proposed in Chapter7is even more promising. Only very few mea-

suredchannel responses (CRs)7 - theoretically only three for a two-dimensional localization

problem - are required to obtain initial parameter estimates of the stochastic location finger-

print model. This estimation method is based on a geometricalUWBchannel model and

exploits a priori knowledge about the geometry of the propagation environment. The perfor-

mance is evaluated with dedicated measurements in a controlled propagation environment.

It is expected that these parameter estimates provide only a partial description of a realis-

tic propagation channel, but can serve as initial parameter estimates for the aforementioned

iterative procedure.

7ACRis defined as convolution of aCIRwith a transmit pulse. If the transmit pulse is a sinc-pulse then CRis identical to CIR.

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Chapter 2

Location Fingerprinting: A

Communication Theoretic Perspective

In this chapter1, a location fingerprinting framework is developed from a communication the-

oretic perspective applying fundamental results from statistical detection theory. This frame-

work generalizes all location fingerprinting methods applying classification algorithms based

on a Bayesian formulation. For example neural networks or support vector machines are not

covered by this framework. The following investigations are done for the two-dimensional

Euclidian space for the sake of visualization. Extensions to three dimensions are straightfor-

ward.

2.1 Problem Formulation

We consider an indoor scenario with a given surveillance area as depicted in Fig.2.1. The

surveillance area is sampled on a grid with Mpoints. During a training phase, location fin-

gerprints denoted bysmand the corresponding coordinates denoted by (x, y)mare gathered

for all m = 1, 2, . . . , M grid points. The set of all location fingerprints and coordinates consti-tutes the location fingerprint database2. In case of remote positioning, this database is stored

at theCU, which also executes the pattern matching algorithm and might additionally act

as anchor. If there exist multiple distributed anchors (cf. Fig.2.1), for example distributed

access points inRSSbased location fingerprinting systems, then all individual location fin-

gerprints observed at each anchor are transmitted to theCUand are stacked intosm. In case

of self-positioning, each agent act asCUand, thus, must have a copy of the database and

1Parts of this chapter have been published in[43].2Such a database is also known as radio map.

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Chapter 2 Location Fingerprinting: A Communication Theoretic Perspective

CU

anchor

anchor

anchoranchor

Fig. 2.1:Grid points within a given surveillance area, anchors and central unit.

has to execute the pattern matching algorithm. The number of components in the vector sm

is denoted byN. Throughout this thesis, it is assumed that the agents transmit (i.e. act as

TXs) and the anchors receive (i.e. act asRXs), which corresponds to the remote positioning

setup. Due to channel reciprocity the roles of agents and anchors are interchangeable, which

implies that this assumption does not reduce generality.

The location fingerprint sm is related to the coordinates (x, y)m and the positions of the

anchors via the corresponding propagation channels. The actual shape ofsm depends on

the signal processing at the agent and anchors, but does not matter for the here proposed

theoretical framework. For example, inRSSbased location fingerprinting systems each

element insmcorresponds to the averageRSSat a specific access point (anchor). Note that

theRSSdepends also on the transmit power of the agent, which implies that the transmit

powers of all agents either have to be known or must be set to the same value. For location

fingerprinting systems employing wideband orUWBsignals,smcould be a sampledCIRor

channel parameters like path delays and gains.

During the localization phase, theCUobserves the vectory from an agent with unknown

position(x, y), which corresponds to remote positioning. The inference of(x, y)based ony

is formulated as anM-ary hypothesis testing problem [44] according to

HypothesisHm:The agent excitingyis located at position(x, y)m.

Note that theCUcould be considered as agent, which would correspond to self-positioning.

Then the hypotheses are reformulated according to

HypothesisHm:The agent observingyis located at position(x, y)m.

Depending on the modeling ofsm, different detection problems can be distinguished.

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2.2 Deterministic Location Fingerprints

2.2 Deterministic Location Fingerprints

The simplest model assumes that sm

is deterministic. Deterministic location fingerprints

are commonly used inRSSbased systems due to the rather stable behavior of the average

RSS,which is mainly influenced by large scale propagation effects such aspath loss (PL)

or shadowing. The advantages of the deterministic formulation are low complexity pattern

matching algorithms, such as Euclidian distance calculation between the observation and

each location fingerprint [30, 45] or the weightedknearest neighbors algorithm [31].

In general, the observation ydoes not correspond exactly to one of the M location fin-

gerprints due to random distortions like thermal noise, interference, and variations of the

propagation channel over time. Therefore, the observations are commonly modeled by

y=sm + n,

where the random vector naccounts for the distortions. This model assumes that the sm

are the true location fingerprints, which implies that the distortions during the training phase

have to be mitigated. This is usually achieved through averaging several location fingerprints

from the same position over time.

Each sm can be interpreted as a constellation point in an N-dimensional signal space.

Thus, there are totally Mconstellation points. ThePDFofygiven Hm is determined by

sm and thePDFofn. ThesePDFsfor all Mhypotheses suffice to derive optimal pattern

matching (classification) algorithms and calculate the corresponding error probability. These

topics are further discussed in Section2.4.

In most cases the unknown position of the agent denoted by(x, y)is not equal to one of the

grid points (x, y)m, which poses an additional source of error. The impact of this deviation on

the performance of the classification algorithm depends on its robustness to spatial variations

of the location fingerprints. In order to combat this problem, the grid spacing can be reduced

and the number of training points increased. This, however, increases the complexity of the

training phase and localization phase. Moreover, the probability of making decision errors

increases as well.

As already mentioned,RSS based location fingerprints can be made robust to temporal and

spatial variations of the propagation channel by averaging theRSSover small scale propaga-

tion effects. On the contrary, widebandCIRsare very sensitive to these small scale effects,

which implies that the deterministic formulation is not applicable to location fingerprints

related toCIRs.

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2.3 Novel Position Location Concept - "Geo-Regioning"

In this section, a novel position location concept based on a stochastic description of the

location fingerprints sm is proposed. The main idea is to relax the requirement of exact

grid coordinates. In the above formulation assuming deterministic location fingerprints, the

objective is to estimate the exact coordinates of an agent. In the here proposed formulation,

the goal is to estimate the region, in which an agent is located in. This is illustrated in

Fig.2.2, where the squares define the regions. Note that there are four grid points in each

region.

CU

anchor

anchor

anchoranchor

Fig. 2.2:Regions of an indoor position location system.

This relaxed problem formulation has some distinct advantages over the deterministic for-

mulation. First, the training coordinates need not be known exactly. It is sufficient to know

that the received training signal is generated by a TXlocated within the considered region.

Furthermore, it is possible to trade off accuracy against complexity. The larger the regions

are chosen, the fewer of them are needed in order to cover the surveillance area. Fewer and

larger regions imply less complexity of training and localization. The drawback of larger

regions is a larger uncertainty area, which determines the fundamental position location in-

accuracy due to the spatial quantization into regions. Assuming a uniform distribution of the

agent positions within these regions, the correspondingRMSerrors can be calculated.

The hypothesis testing problem for remote positioning is reformulated according to

HypothesisHm:The agent excitingyis located in regionm.

In case of self-positioning the hypotheses are stated as

HypothesisHm:The agent observingyis located in regionm.

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2.3 Novel Position Location Concept - "Geo-Regioning"

Since the location fingerprints represent now an area3 instead of a grid point, it is essential

to model the spatial small scale behavior of the location fingerprints. Consequently, we pro-

pose stochastic location fingerprints and assume that there exists a parameterized PDF, which

models the behavior of the location fingerprints over space. ThisPDFdepends on the shape

of the location fingerprints, i.e. on the signal processing atTXandRX,the dimensions of the

regions, and the assumptions about the propagation channel. Different regions/hypotheses

are distinguished by the parameters of thisPDF.These parameters need to be estimated dur-

ing the training phase for each region. The database consists ofMparameter sets denoted by

mwith the corresponding coordinates (x, y)m, which represent the centers of the regions.

ThePDFofyis determined by thePDFofsmand thePDFofn.

The following fundamental questions arise:

1. How should the location fingerprintssmbe chosen?

2. What parameterizedPDFshould be used to model these location fingerprints?

3. Which parameters of thisPDFare relevant to distinguish the regions?

4. What performance can be achieved in a dense multipath and non-LoSpropagation

environment?

5. What is the impact of system parameters on performance and complexity of the loca-

tion fingerprinting system?6. How much training data is needed to obtain accurate parameter estimates such that a

desired performance is achievable?

7. How can the efficiency of the training phase be improved?

In the course of this thesis, these questions will be answered.

In the next section, we complete the location fingerprinting framework by defining two

figures of merit for the position location and clustering problem, and by deriving the corre-

sponding optimal classification algorithms.

3In the three-dimensional case they represent a volume.

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2.4 Location Fingerprinting as Hypothesis Testing Problem

We start the discussion by repeating the hypotheses:

HypothesisHm:The agent excitingyis located at (x, y)m , (2.1)

where(x, y)m can be interpreted as exact position (cf. Section2.2) or as the center of a

region (cf. Section2.3).

If we are not interested in the physical position, but rather in a clustering of a wireless

network, then it is sufficient to formulate the hypotheses as

HypothesisHm:The node excitingyis located in clusterm. (2.2)

We refer to (2.1) as position location problem and to (2.2) as clustering problem.

In order to solve the hypothesis testing problem, the Bayesian paradigm [46] is followed.

It is assumed that a priori probabilities denoted by 1, 2, . . . , Mcan be assigned to the

hypotheses. These a priori probabilities can be considered as relative number of agents

located in each region. If these a priori probabilities are unknown, then they are set to 1/M.

The average cost or Bayes risk (R) is defined as [44, 46]

R =Mi=1

Mj=1

jCi,jP (Hi|Hj) =Mi=1

Mj=1

jCi,j

Zi

fj(y|Hj) dy, (2.3)

whereP(Hi|Hj) is the probability of deciding for Hi, when Hj is true, fj(y|Hj)4 is theconditionalPDFofygivenHj , andZidefines the part of the observation space in whichHi

is chosen. The parametersCi,j denote the costs for deciding forHiwhenHjis true.

Following the derivations in [46], the decision rule minimizing (2.3) is found as

m= argminm=1,2,...,M

Mj=1

Cm,jP(Hj |y) ,

where m denotes the estimate for the true hypothesis and P (Hj|y) is the a posteri-ori probability of Hj given observation y. Applying Bayes rule and noticing that

f(y) =M

m=1 mfm (y|Hm) does not depend on m, an equivalent decision rule is given4The conditioning onHj determines the parameter set j .

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by


M

j=1jCm,jfj (y|Hj) . (2.4)

In the following two sections, we define two performance measures, which are used for the

position location problem and for the clustering problem, respectively.

2.4.1 Average Positioning Error

The figure of merit for the position location problem is the average positioning error, which

is defined as

De M

j=1

jMi=1

di,jP (Hi|Hj) =M

j=1

j

dj,jP(Hj|Hj) + M

i=1,i=j

di,jP (Hi|Hj)

=M

j=1

jdj,j+M

j=1

jM

i=1,i=j

(di,j dj,j) P(Hi|Hj) , (2.5)

wheredi,j =dj,i is the Euclidian distance between the center points (x, y)i and(x, y)j of

regionsiandj. For this derivation we have used the fact thatMi=1 P(Hi

|Hj) = 1. We notice

that the average positioning error results from Bayes risk by setting the costs Ci,j equal to

di,j . Thus, if alldi,j are known a priori between all regions, then the decision rule


Mj=1

jdm,jfj(y|Hj) (2.6)

minimizes De. Note that we can account for the fundamental position location inaccuracieswithin the regions by assigning non-zero values to dj,j . This is especially important, if

different regions have different dimensions. The values for dj,jand jdetermine the minimal

average positioning error, which is achieved if all conditional error probabilities P (Hi|Hj)fori =jare zero.

2.4.2 Total Probability of Error

When considering the clustering problem, thedi,j are not relevant. Therefore, the costs of

wrong decisions are set to one (Ci,j= 1fori =j) and the costs of correct decisions are set tozero (Ci,i= 0). This assignment leads to a minimization of the total probability of error [44],

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which is given by

Pe =M

j=1j

M

i=1,i=j P (Hi|Hj) . (2.7)

The decision rule, which minimizes (2.7) is found by inserting the assumptions on

the costs into (2.4) and by simplifying the expression, which results in the M-ary

maximum a posteriori probability (MAP)decision rule

m= argmaxm=1,2,...,M

P (Hm|y) = argmaxm=1,2,...,M

mfm (y|Hm) . (2.8)

For equally likely hypotheses, i.e. m

= 1/Mfor all m, this rule simplifies further to the

M-aryMLdecision rule.

By defining the likelihood ratios i (y)fori= 1, 2, . . . , M as

i (y) = fi (y|Hi)f1 (y|H1) , (2.9)

theM-aryMAPdecision rule can be reformulated as

ii (y)m=j

m=ijj(y) fori, j= 1, 2, . . . , M andi > j. (2.10)

TheM 1likelihood ratios i (y) fori= 2, 3, . . . , M define the coordinate system of the(M 1)-dimensional decision space and the M(M 1) /2decision rules in (2.10) definethe(M2)-dimensional hyper planes, which are the boundaries of the decision regions. ForM= 2 the decision space is one-dimensional and there exists one decision threshold. For

M= 3the decision space is two-dimensional and the three decision boundaries are straight

lines, which define decision areas. For M= 4 the decision space is three dimensional and

the six hyper planes are planes.

Applying all M(M 1) /2decision rules in (2.10) to an observation vector yproducesthe MAPestimate m for the true hypothesis. Depending on the particular expressions

forfm (y|Hm)the likelihood ratios in (2.9) can be considerably simplified, which reducesthe complexity of theMAPdecision rule and mitigates numerical problems due to a poten-

tially high dimensionality ofy. Therefore, the decision rule stated in (2.10) might be easier

to implement than the original decision rule stated in (2.8).

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2.4.3 Location Fingerprinting with Multiple Observations per Agent

In a realistic position location scenario, it is conceivable that the CUhas multiple observa-

tions from each agent available for the localization (region detection) process. The essential

assumption is that these multiple observations are caused by an agent, which is located in

oneregion.

For example the agent could be equipped with multiple antennas and could use them

either sequentially to transmit its signals to the anchors or use orthogonal signals to trans-

mit them simultaneously. Furthermore, if the agent is mobile it can transmit signals peri-

odically always from a slightly different position. These are just two examples how such

multiple observations could be generated. Note that the same ideas can be also applied toself-positioning.

In the following, we derive the optimal decision rule taking multiple observations into

account. TheCU has recorded K observations{y1, . . . ,yK}. It is assumed that these ob-servations are independent and are caused by an agent located in the same region. The

individual observations are stacked into a larger vectory=

yT1 , . . . , yTK

T. The conditional

PDFofyis given by the product of the individualPDFsofykaccording to

fm (y|Hm) =Kk=1

fm (yk|Hm) . (2.11)

This follows from the assumption that the individual observations are independent. By in-

serting thePDFsfor ygivenHminto (2.6) or (2.8) we can modify the decision rules such

that multiple observations are exploited.

2.4.4 Pairwise Error Probabilities

For most decision problems with largeM, it is mathematically intractable to obtain analytic

expressions for Deor Pedue to complex decision regions in an (M1)-dimensional space.In order to circumvent this issue, it is useful to assume that only two hypotheses, say Hiand

Hj , are possible. The corresponding binary decision rule following the Bayesian paradigm

is given by

l function

fi (y|Hi)fj(y

|Hj)

m=i

m=ji,j ,

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which is a threshold test on the sufficient statistic l. A sufficient statistic is a function of

the observation y which has the property that the likelihood ratio fi(y|Hi)fj(y|Hj)

can be written

as a function of the sufficient statistic [44]. The thresholdi,j

depends on the considered

performance measure. ForPe it is given by i,j = ji and forDe it is i,j = j(di,jdj,j)i(dj,idi,i)

.

The sufficient statisticlis itself a random variable and has aPDFdenoted byfl|Hj(l), if it is

assumed thatHj is the true hypothesis.

Considering the binary hypothesis testing problem, the pairwise error probabilities are

defined by

P (Hj

Hi)

i,jfl|Hj(l) dland P (Hi

Hj)

i,j

fl|Hi (l) dl. (2.12)

The quantity P (Hj Hi) is the probability of deciding for Hi, when Hj is true and noother hypotheses are possible. Note that the pairwise error probabilities are in general not

symmetric, i.e. P (Hj Hi) =P (Hi Hj). The pairwise error probabilities can be usedto upper bound both performance measures by applying the union bound [47], which gives

De M

j=1

jdj,j+M

j=1

jM

i=1,i=j

(di,j dj,j) P(Hj Hi) ,

Pe M

j=1

jM

i=1,i=j

P (Hj Hi) . (2.13)

If we can derive analytical expressions for P (Hj Hi), we can provide analytical upperbounds for the performance of the position location or clustering problem without perform-

ing time consuming Monte Carlo simulations. Furthermore, analytical error expressions

usually provide insights into fundamental effects determining the performance and are vi-

able tools to optimize system parameters.

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Chapter 3

Channel Measurement Campaign

This chapter describes aUWBchannel measurement campaign, which is designed to demon-

strate the feasibility of the proposed location fingerprinting method and evaluate its perfor-

mance in a dense multipath propagation environment with non-LoS conditions. A more

detailed description of this measurement campaign can be found in [48]. Note that we do

not specify the type of the location fingerprints smyet, but they will be extracted from the

measuredCIRsobtained by this campaign.

3.1 Measurement Setup

The measurements were performed in a cellar room (cf. Fig.3.1) with a size of about

7.4m times15m and a height of6m. There are many metallic objects in the room such

as metallic shelves, heating pipes, cabinets and metal cores, implying a dense multipath en-

vironment with some non-LoSsituations. The propagation environment was kept mostly

static during the measurements, although people, who performed the measurement, were

always present and sometimes moving.

A time-domain correlation method was used to estimate the CIRs. The principle is toperform a cross-correlation between the received signal and the known transmit signal at the

RX. In practice, the transmit signal is often generated usingpseudo noise (PN)bit streams

or m-sequences. The transmit signal is fed to apower amplifier (PAMP)and finally to the

transmit antenna. This signal propagates through the channel, is received by the receive

antenna, amplified by anlow noise amplifier (LNA), and sampled by an oscilloscope with

a sampling frequency of20GHz. The measurement frequency range was roughly limited

from3GHz to6GHz by the transfer functions of theUWBantenna,PAMP,LNA,and input

filter of the oscilloscope. The reference signal for the cross-correlation, i.e. the transmit

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Chapter 3 Channel Measurement Campaign

signal, was pre-stored in the oscilloscope, such that no wired connection between TXand

RXwas required. This implies, however, that the absolute time references are unknown.

Thus, each measuredCIRhas an unknown time shift. Furthermore, the impulse responses

of the transmit and receive antenna are comprised in the measuredCIRs,which is further

discussed in Section3.3.

3.2 Measurement Scenario

A large number ofCIRsbetween one staticRXequipped with four antennas and a mobileTX

also equipped with four antennas has been measured. TheRXacts asCU.The height ofTX

andRXantennas was chosen as1.8m. The receive antennas were mounted in the corners ofa square with a side length of38cm and the transmit antennas were mounted in the corners

of a square with a side length of20cm on a two-dimensional positioning device. This device

allows to move theTXarray within an area of27cm times56cm. The positioning device

was moved to22 different locations. These locations define the center points (x, y)mof the

M= 22regions, which are depicted in Fig.3.1.The maximum distance between two regions

is approximately17m, whereas the minimum separation of two transmit antenna positions in

two different regions is approximately10 cm. In AppendixAthe complete distance matrix

collecting the distancesdi,j between all center points is listed.TheTXarray was moved with an almost constant speed of1cm/s within each region.

The trigger at the oscilloscope was not synchronized with the movement of the TXarray,

which means that the exact positions of theTXantennas are unknown. However, since

triggering was done periodically every 1.7s, the spacing of subsequent measuredCIRsis

approximately1.7cm. Roughly155trigger events were performed implying2480measured

CIRsper region.

Fig.3.2depicts the received signal at receive antenna 3after cross-correlation with the

referencePNbit stream. The four visibleCIRsorigin from four time-shifted transmit signalsat the four transmit antennas.

3.3 Impact of Antennas

The measuredCIRscomprise the patterns and the transfer functions of the transmit and

receive antennas. Skycross SM3TO10MA antennas, as depicted in Fig.3.3, were used for

the measurements.

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3.3 Impact of Antennas

15

m

7.4m

56

cm

27cm10cm

Fig. 3.1:Measurement scenario: Regions, propagation environment, and RX.

0 500 1000 1500 20004

3

2

1

0

1

2

3

4x 108

t[ns]

h(t)

Fig. 3.2:Output of the cross-correlation at receive antenna 3.

These antennas are specified to work in the frequency range from 3.1to10GHz. Further-

more, the data sheet1 claims that these antennas are omnidirectional in the azimuth plane,

1SM3TO10MA data sheet is online available at www.skycross.com/Products/PDFs/SMT-3TO10M-A.pdf.

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Fig. 3.3:Skycross SM3TO10MA UWB antenna.

which is defined as the plane perpendicular to the axis of the antenna. The measured antenna

patterns in the azimuth plane for different frequencies are depicted in Fig. 6.1 on page 59

in [49]. It can be concluded from these measurement results that the largest gain difference

is approximately 5dB, which occurs between the azimuth angles 90 degrees and270 de-

grees. Further, it can be concluded that the antenna gain stays roughly constant for small

changes in the azimuth angle.The orientations of the receive antennas were fixed during the whole measurement cam-

paign. Further, the transmit antennas were mounted with fixed orientations on the positioning

device. Due to the movement of this device within each region the orientations of the trans-

mit antennas were only slightly changing. Therefore, it is assumed that the influence of the

antenna patterns on theCIRsmeasured in each region is negligible.

3.4 Measurement Signal-to-Noise Ratio

The thermal noise due to theLNAand the electronics of the oscilloscope is assumed to

be an additive zero mean white Gaussian noise process. The corresponding noise samples

are therefore Gaussian distributed with zero mean and variance 2mea, which is given by

the room temperature, the noise figures of theLNAand oscilloscope, and the measurement

bandwidth. The measurementSNRis denoted by SNRmea and is defined as the average

energy of theCIRswithin one region divided by22mea. The measurementSNRranges from

45dB to55dB depending on the distances between the center points of the regions and the

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3.5 Energy Normalization

RX. Due to this high measurementSNR,it is assumed that the measuredCIRsare essentially

distortion-free.

3.5 Energy Normalization

In order to remove the dependence of the location fingerprints on the transmit power of the

agents, the average energy ofCIRswithin one region is normalized to the same value for

all regions. This is necessary, whenever it cannot be guaranteed that all agents use the same

transmit power. For example this can happen, when the data rate is adapted to the current

work load or channel conditions. It is important to notice that energy normalization impliesthat thePLinformation is not used for position location.

3.6 Temporal Alignment

The measurement setup does not provide absolute timing information, which means that

there exists an unknown time offset for each measuredCIR. We have already pointed out

that signal metrics related to the direct path are not required for location fingerprinting. How-ever, we require some sort of temporal alignment of the measuredCIRs,in order to obtain

meaningful location fingerprints and estimate meaningful statistical parameters.

In every wireless communication system, theRXneeds to synchronize its symbol timing

to the symbol timing of theTX. Such a synchronization algorithm would be responsible

for the temporal alignment task in a realistic RX implementation. In the following, simple

temporal alignment strategies are discussed.

3.6.1 Problem Formulation

We consider a sampled received signal in an observation window [0, K1]denoted byrandassume that theCIRdenoted byh of lengthN < Kis located somewhere within the obser-

vation window. The objective is to identify a reference sample, estimate it for each measured

CIRand shift the time axis accordingly such that all measured CIRshave a common time

reference. Such a reference sample could be, for example, the sample with the maximum

absolute value.

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3.6.2 Maximum Absolute Value Alignment

The simplest strategy is to identify the sample with the maximum absolute value as the

reference sample. This can be written as

nmaxabs = argmaxn{0,...,K1}

|r[n]|.

Depending on theSNR, the noise samples present in r may produce large variations in

nmaxabs. Thus, this alignment strategy requires a highSNR.

InLoSsituations, theCIRsare most likely aligned to the direct path, which implies that

samples before the reference sample are only noise samples. However, in case of a non-

LoSsituation, theCIRsare aligned to the strongest path, which is not necessarily the direct

path. This means that also samples before the reference sample can carry significantCIR

energy and contain position location information. There is a trade-off between accounting

for possible non-LoSsituations and wasting samples by accounting for noise-only samples.

In general, it can be assumed that the position location system can afford moreRXcom-

plexity, for example a higher SNR, during the training phase than during the localization

phase. Therefore, we restrict theSNRanalysis to the localization phase and assume that

we can provide SNRmea during the training phase. Thus, the temporal alignment ofCIRs

utilized during the training phase is done at SNRmea.

Time-of-Arrival Alignment A more sophisticated temporal alignment strategy is to iden-

tify the reference sample as first sample in h, i.e. h[0]. The first sample h[0] is usually

interpreted asToAof theCIR. The interested reader is referred to [6, 22, 23] for a detailed

discussion of various methods with different complexities for ToAestimation. The simula-

tion results provided in this thesis consider exclusively maximum absolute value alignment

as discussed above.

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Chapter 4

Location Fingerprinting with a Coherent

Receiver

In this chapter1, location fingerprinting with a singleanchor using acoherentRXis studied.

TheRXis called coherent, because it can performCIR estimation. Note that we do not

require anything from the agents except from being able to send a training sequence with a

certain bandwidth forCIRestimation. Especially time synchronization between agents and

RXis not required. Thus, the whole complexity of the position location system is shifted to

the anchor, which also acts asCUin accordance to the framework developed in Chapter2.

We adopt the formulation of stochastic location fingerprints proposed in Section 2.3, which

means that the location fingerprintssmwithin each regionmare modeled by aPDFwith pa-

rameter setm. In the course of this chapter, we will answer some of the fundamental ques-

tions raised in Chapter2. The first two questions, which are treated in Sections4.1and4.2,

are concerned with the choice of the location fingerprints and with an accurate and mathe-

matically tractable stochastic description of them.

1Parts of this chapter have been published in[50, 51].

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Chapter 4 Location Fingerprinting with a Coherent Receiver

4.1 Choice of the Location Fingerprints

A physical multipath propagation channel with L paths can be interpreted as tapped delay

line [52] withLtaps according to

h(t, ) =Ll=1

l(t)( l(t)),

wherel(t)is the time-varying gain andl(t)is the time-varying delay of path l. Time vari-

ations of gains and delays are caused by movement ofTXorRX(or both) and/or movement

of objects in the environment.

Since any wireless transmission system is band-limited, the continuous time CIRof interest is as well and can be represented by discrete-time samples denoted by

h[t, n] hband-limited

t, nfs

withfsas the sampling rate. Iffsfulfills the sampling theorem,

the continuous timeCIRcan be recovered by interpolation with time-shifted sinc functions.

We consider an equivalent baseband representation of the continuous timeCIR,which

implies complex valued samples h[t, n]. Since the equivalent baseband samples provide a

complete description of the continuous timeCIR, it is proposed to use these samples within

an observation window as location fingerprint and definesmwith lengthNaccording to

sm (t) [hm[t, 0], hm[t, 1], . . . , hm[t, N 1]]T ,

where the subscriptmdenotes the agents region. Thus,hm[t, n]denotes then-th sample of

an equivalent basebandCIRfrom an agent located in regionmobserved at time instant t.

The time dependency of these samples is still considered, which causes time-varying location

fingerprints. Due to the time windowing, the continuous timeCIRcannot be reconstructed

based onsm (t)without error. The observation window should be chosen such that the main

part of theCIRenergy is captured. Furthermore, it is assumed that sm (t)does not change

int during one observation window. Since the observation duration is typically in the order

of tens of nanoseconds, this is assumption is well justified in indoor scenarios due to the

limited speed of TX, RX, and objects in the environment.

Iffsis larger than Nyquist rate this corresponds to oversampling, which provides a redun-

dant representation of the continuous timeCIR. This implies that the length ofsmincreases

for the same observation window duration and, consequently that more statistical parameters

have to be estimated. This, in turn, increases the complexity of the training phase without

increasing the information content. Thus,fsis chosen as Nyquist rate.

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4.2 Regional Channel Model


For design, implementation, and evaluation of a location fingerprinting system, a statisticalmodel ofsm (t)is required. The statistical description should be robust to time-variations

caused by a randomly changing propagation environment, for example, by moving people.

More importantly, we have to accurately model the variations of the location fingerprints

within a small region of space. This change in position in the order of a few multiples of the

carrier wavelength causes small scale fading of the samples h[t, n], which can be modeled

with various probability distributions [52,53]. In the following we use the terms channel taps

and samples interchangeably.

A common assumption on the small scale fading behavior of equivalent baseband channeltaps is that they are complex Gaussian distributed. The justification of this assumption is

given by the central limit theorem. Many reflected and scattered partial waves of similar

average power from different directions superimpose at the receive antenna and contribute

to one channel tap. If the number of partial waves is large enough, the central limit theo-

rem can be applied and the resulting distribution of the channel tap can be assumed to be

Gaussian [54, 55]. However, as the sampling frequency becomes larger due to increasing

signal bandwidth (approaching UWB bandwidths) less of these partial waves contribute to

one channel tap. This fact questions the applicability of the central limit theorem.

In literature, there exist various studies on the tap statistics for UWB channels. For the tap

amplitudes, the Nakagami-m [56], Log-normal [49, 57], and Weibull [58] distributions are

proposed. However, also Rayleigh and Rice amplitude distributions arising from a complex

Gaussian channel model are supported by some channel measurement campaigns [59, 60].

The phase distribution of the channel taps is commonly assumed to be uniform between and.

In the next section, we apply Akaikes information criterion (AIC)[61] to channel tapsobtained by the measurement campaign described in Chapter 3, in order to find the best

distribution out of a candidate set for the modeling of the small scale fading behavior. A

short review ofAICcan be found in AppendixB.Furthermore, thorough discussions about

UWBchannel modeling can be found in [52, 53, 60, 62, 63]. TheAICis applied to chan-

nel taps after measurement post-processing steps in the following order: Passband filtering

from3to6GHz, equivalent baseband transformation, threefold interpolation (upsampling to

60GHz sampling rate), temporal alignment, downsampling to Nyquist rate (downsampling

to3GHz sampling rate), and energy normalization.

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Chapter 4 Location Fingerprinting with a Coherent Receiver

4.2.1 Marginal Distribution of Channel Taps

The considered ensemble consists of all measuredCIRsfrom one region (all four transmit

antennas) to receive antenna 3. The number ofCIRsin this ensemble is 620. Region2

withLoS CIRsand region 18 with non-LoS CIRsare chosen for presentation in this sec-

tion. Further investigations show that the obtained results and drawn conclusions hold for all

other regions as well. Although the measurement process for one region lasted for roughly

250 seconds, it is assumed that the ensemble is measured at a single time instant t= t0.

Thus, the time dependency of the location fingerprints is omitted in the following considera-

tions. The propagation environment was kept mostly static during the measurements, which

justifies this assumption.

0 50 100 15050

40

30

20

10

0

Region2Region18

n

10log10

(PDP[n])

Fig. 4.1:Normalized PDPs in dB for regions2and18.

Fig.4.1depicts the normalizedpower delay profiles (PDPs)for regions 2and 18in dB.

The reference sample is set tonmaxabs= 31. It can be seen that samples before the reference

sample carry significantCIRenergy for region18, which is not the case for region 2. The

observation window has a duration of60ns, which corresponds to N= 180samples obtained

with3GHz Nyquist sampling.

Amplitude Distribution The candidate set consists of the following six distributions:

Nakagami-m, Log-normal, Weibull, Gamma, Rayleigh, and Rice. All distributions have

two parameters except for the Rayleigh distribution, which has only one parameter. This

choice is based on channel modeling literature as discussed above. Fig.4.2and Fig.4.3

depict the respective Akaike Weights for all fitted candidate distributions for region 2and

region18. The Akaike Weights (cf. AppendixB) are estimates for the probability that the

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0 20 40 60 80 100 120 140 160 1800

0.5

1

0 20 40 60 80 100 120 140 160 1800

0.5

1

0 20 40 60 80 100 120 140 160 1800

0.5

1

0 20 40 60 80 100 120 140 160 1800

0.5

1

0 20 40 60 80 100 120 140 160 1800

0.5

1

0 20 40 60 80 100 120 140 160 1800

0.5

1

n

Nakagami-m

Log-normal

Weibull

Gamma

Rayleigh

Rice

AkaikeWeightsfor|h[n]|

Fig. 4.2:Akaike Weights for tap amplitudes |h[1]|, |h[2]|, . . . , |h[180]| for CIRs from region 2.

location fingerprinting for uwband systems

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